A research group attaches a torque sensor to a rotor (moment of inertia 0.20 kg·m²)…
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Torque and Rotational Dynamics · Torque and Rotational Dynamics
Problem
A research group attaches a torque sensor to a rotor (moment of inertia 0.20 kg·m²) and records the net external torque every 0.50 s for the first 4.0 s after the rotor is started from rest. The measurements are shown in the table.
Time t (s)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Torque τ (N·m)
0.0
3.0
5.5
7.0
6.5
5.0
2.5
0.0
−1.0
Positive torque is ccw.
(a) Using the data, estimate the angular impulse delivered to the rotor from t = 0 to t = 4.0 s by assuming the torque in each 0.50 s interval is equal to the torque value at the beginning of that interval.
(b) Determine the rotor’s angular speed at t = 4.0 s.
(c) Describe one modification to the data-analysis method in part (a) that could yield a more accurate estimate of the angular impulse, and explain why it would improve the result.
(d) Immediately after t = 4.0 s the only external torque on the rotor is a constant friction torque of −0.50 N·m. Calculate the additional time required for the rotor to come to rest.
(e) Discuss two potential sources of systematic error in the torque measurements and propose a calibration step or experimental change that could reduce each error.